Fractal characterization of fracture surfaces in concrete

Saouma, Victor E.; Barton, Christopher C.; Gamaleldin, Negad A.

doi:10.1016/0013-7944(90)90182-g

Cited by 131 publications

(35 citation statements)

References 2 publications

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“…To investigate numerically the properties of the ubiquitiform fracture energy, concrete materials presented in Swartz and Kan (1992) as well as by Saouma et al (1990Saouma et al ( , 1991 and Saouma and Barton (1994) are used. The corresponding material properties as well as the calculated values of δ min from Eq.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…1. Ubiquitiformal fracture energy G uf for concrete: (a) Swartz and Kan (1992), (b) Saouma et al (1990Saouma et al ( , 1991, Saouma and Barton (1994) materials, because the relation for fracture toughness is derived from rationalistic deduction on the assumption of linear elasticity. It seems now that the above mentioned discrepancy can be reasonably explained based on the ubiquitiformal fracture energy as follows.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…As is well known, pioneered by the work of Mandelbrot et al (1984), the fractality of fracture surfaces in various kinds of materials such as concrete (Saouma et al, 1990;Saouma and Barton, 1994), steel (Mandelbrot et al, 1984;Underwood, 1986), ceramic (Mecholsky, 1989) and rock (Krohn and Thompson, 1986; Radlinski et al, 1999) has been verified experimentally, which has gradually lead to the establishment of the emergent fractal fracture mechanics over the past three decades. Naturally, it is a reasonable desire that some important physical concepts or parameters in the classical fracture mechanics can be extended directly into the fractal one but, unfortunately, this is not the case sometimes.…”

Section: Introductionmentioning

confidence: 95%

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Ubiquitiformal fracture energy

Yang

et al. 2017

jtam

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The ubiquitiformal fracture energy is proposed in the paper and its explicit expression is obtained. Moreover, the numerical results for concrete are found to be in good agreement with those for the critical strain energy release rate. The discrepancy between the numerical results of the traditional fracture energy and the critical strain energy release rate can be explained reasonably, which implies that the ubiquitiformal fracture energy should be taken as an available fracture parameter of materials. Finally, it is numerically found for some concrete that there is not size effect for the ubiquitiformal fracture energy.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

See 1 more Smart Citation

Ubiquitiformal fracture energy

Yang

et al. 2017

jtam

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“…) has been studied intensively. It has been proposed that the crack surface fractality might be an alternative source of the observed size effect (Carpinteri 1994;Carpinteri et al 1993Carpinteri et al , 1995Lange et al, 1993, and Saouma et al, 1990, 1994. This paper outlines a generalized asymptotic theory of scaling of quasibrittle fracture and also explores the possible role of the crack surface fractality in the size effect.…”

Section: Introductionmentioning

confidence: 96%

Scaling in Nonlinear Fracture Mechanics

Bažant¹

1997

IUTAM Symposium on Nonlinear Analysis of Fracture

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Abstract. The paper l presents a review of recent results on the problem of size effect (or the scaling problem) in nonlinear fracture mechanics of quasibrittle materials and on the validity of recent claims that the observed size effect may be caused by the fractal nature of crack surfaces. The problem of scaling is approached through dimensional analysis and asymptotic matching. Large-size and small-size asymptotic expansions of the size effect on the nominal strength of structures are presented, considering not only specimens with large notches (or traction-free cracks) but also structures with no notches. Simple size effect formulas matching the required asymptotic properties are given. Regarding the fractal nature of crack surfaces, it is concluded that it cannot be the cause of the observed size effect.

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“…. The experimental results show that a general conclusion cannot easily be drawn [9]: some studies report a positive variation of fracture toughness along with the fractal dimension [6,[10][11][12][13], and others a negative one [14][15][16][17]. To other researchers, there is either no correlation [18][19][20] or the fractal dimension of the fractured surfaces is a universal constant [21].…”

Section: Introductionmentioning

confidence: 98%

Statistical artefacts in the determination of the fractal dimension by the slit island method

Bigerelle

Iost

2004

Engineering Fracture Mechanics

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. AbstractThis paper comments upon some statistical aspects of the slit island method which is widely used to calculate the fractal dimension of fractured surfaces or of materialsÕ features like grain geometry. If a noise is introduced when measuring areas and perimeters of the islands (experimental errors), it is shown that errors are made in the calculation of the fractal dimension and more than a false analytical relation between a physical process parameter and the fractal dimension can be found. Moreover, positive or negative correlation with the same physical process parameter can be obtained whether the regression is performed by plotting the variation of the noisy area versus the noisy perimeter of the considered islands or vice versa. Monte-Carlo simulations confirm the analytical relations obtained under statistical considerations.

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Fractal characterization of fracture surfaces in concrete

Cited by 131 publications

References 2 publications

Ubiquitiformal fracture energy

Ubiquitiformal fracture energy

Scaling in Nonlinear Fracture Mechanics

Statistical artefacts in the determination of the fractal dimension by the slit island method

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